# 11.2.2 - Minitab Express: Goodness-of-Fit Test

## Research Question: Section

When randomly selecting a card from a deck with replacement, are we equally likely to select a heart, diamond, spade, and club?

I randomly selected a card from a standard deck 40 times with replacement. I pulled 13 hearts, 8 diamonds, 8 spades, and 11 clubs.

## MinitabExpress – Conducting a Chi-Square Goodness-of-Fit Test

### Summarized Data, Equal Proportions Section

To perform a chi-square goodness-of-fit test in Minitab Express using summarized data we first need to enter the data into the worksheet. Below you can see that we have one column with the names of each group and one column with the observed counts for each group.

Suit Count Hearts 13 Diamonds 8 Spades 8 Clubs 11
1. On a PC: Select STATISTICS > Chi-Square Goodness-of-Fit
On a Mac: Select Statistics > Tables > Chi-Square Goodness-of-Fit
2. From the drop-down box select Summarized data in a column
3. Double-click Count to enter it into the Observed Counts box
4. Double-click Suit to enter it into the Category names box
5. Click OK

This should result in the following output:

Chi-Square Goodness-of-Fit Test: Count
Observed and Expected Counts
Category Observed Test
Proportion
Expected Contribution
to Chi-Sq
Hearts 13 0.250000 10 0.90
Diamonds 8 0.250000 10 0.40
All expected values are at least 5 so we can use the chi-square distribution to approximate the sampling distribution. Our results are $$\chi^2 (3) = 1.80$$. $$p = 0.6149$$. Because our p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis. There is not evidence that the proportions are different in the population.